PRESSURE-TEMPERATURE LIMIT CURVES

PRESSURE-TEMPERATURE

LIMIT CURVES

Carlos Cueto-Felgueroso

18/09/2018 1

Training School, 3 - 7 September 2018

Polytechnic University of Valencia (Spain)

This project received funding under the Euratom research and training

programme 2014-2018 under grant agreement Nº 661913

A primary goal in the design, fabrication and

operation of nuclear power plants is to ensure that

the likelihood of fracture of pressure-retaining

components in the reactor coolant boundary is

acceptably low

Regulations and Codes and Standards (C&S)

contain requirements to achieve such a goal:

• Requirements for materials

• Rules for design

▪ Including also analytical procedures based for on fracture

mechanics for the prevention of brittle fracture

• Welding and NDE

• …

Introduction

03/09/2018 2SOTERIA Training School - September 2018 - Polytechnic University of Valencia

During operation, the reactor is operated within

explicit pressure-temperature (P-T) limits to ensure

that acceptable margins against failure are

maintained during normal reactor heat-up and

cooldown, and pressure tests

This presentations cover the US requirements for the

development of P-T limits

These requirements are applied for the Spanish NPPs

of US design

Introduction (cont.)

3SOTERIA Training School - September 2018 - Polytechnic University of Valencia03/09/2018

“The pressure-retaining components of the reactor

coolant pressure boundary that are made of ferritic

materials must meet the requirements of the ASME

Code, supplemented by the additional requirements

set forth below, for fracture toughness…. For the

reactor vessel beltline materials, including welds,

plates and forgings, the values of RTNDT and Charpy

Upper-Shelf Energy must account for the effects of

neutron radiation….”

The “additional requirements” referred to above are

the following ones:

Fracture toughness requirements of

10 CFR 50, Appendix G


Minimum Charpy Upper-Shelf Energy (USE) requirements

P-T limits for heat-up, cooldown, and test conditions

must be at least as conservative as those obtained by

following Appendix G of ASME Code Section XI

Additional safety margins (beyond ASME) when the

reactor core is critical

Minimum temperature requirements determined by the

RTNDT of the RPV closure flange materials


10 CFR 50, Appendix G (cont.)



10 CFR 50 Appendix G (cont.)

6

Operating conditionVessel

pressure1

Requirements for pressure-

temperature limits

Minimum temperature

requirements

1. Hydrostatic pressure and leak tests (core is not critical):

1.a Fuel in the vessel <20% ASME Appendix G Limits (2)

1.b Fuel in the vessel >20% ASME Appendix G Limits (2) + 90 °F(6)

1.c No fuel in the vessel

(Preservice Hydrotest Only)ALL (Not Applicable) (3) + 60 °F

2. Normal operation (incl. and cool-down), including anticipated operational occurrences:

2.a Core not critical <20% ASME Appendix G Limits (2)

2.b Core not critical >20% ASME Appendix G Limits (2) + 120 °F(6)

2.c Core critical <20% ASME Appendix G Limits + 40 °F. Larger of [(4)] or [(2) + 40 °F]

2.d Core critical >20% ASME Appendix G Limits + 40 °F. Larger of [(4)] or [(2) + 160 °F]

2.e Core critical for BWR (5) <20% ASME Appendix G Limits + 40 °F. (2) + 60 °F

1. Percent of the preservice system hydrostatic test pressure.2. The highest reference temperature of the material in the closure flange region that is highly stressed by the bolt preload.3. The highest reference temperature of the vessel.4. The minimum permissible temperature for the inservice system hydrostatic pressure test.5. For boiling water reactors (BWR) with water level within the normal range for power operation.6. Lower temperatures are permissible if they can be justified by showing that the margins of safety of the controlling region are equivalent to those required for the beltline when it is controlling.

SOTERIA Training School - September 2018 - Polytechnic University of Valencia03/09/2018

10 CFR 50 Appendix G P-T limits are just one of many

P-T limits constraining plant operations

• Reactor coolant pump net positive suction head (NPSH)

• Margin for saturation

• Steam generator operating limits

• RCP seal differential pressure

• RHR Relief valve

• Low Temperature Overpressurization Protection (LTOP) Systems

• …

Operating window


Operating window


ASME Code Section III, Appendix G fracture

mechanics method was introduced in 1972 for

preventing brittle fracture in design and for initial

plant operating P-T Limit Curves

▪ Large (1/4-thickness depth) assumed reference flaw

▪ Lower bound fracture toughness (KIR)

▪ Safety Factor of 2 on primary stresses (e.g., those due to

pressure)

▪ Safety Factor of 1 for thermal stresses (due to their self-

relieving nature)

▪ Predicted irradiation embrittlement during the design

life must be also taken into account

ASME Appendix G


It is an axial (¼-thickness depth) sharp surface defect

▪ Semi-elliptical: length equal to 6 times the depth

▪ Final defect

• No fatigue crack growth necessary

Reference flaw

10

¼ T

¾ T

T


In ASME Section III Appendix G the reference

fracture toughness 𝐾𝐼𝑅 has been used

Fracture toughness KIR

11SOTERIA Training School - September 2018 - Polytechnic University of Valencia

• 𝐾𝐼𝑅 is the critical, or

reference, stress

intensity factor as a function of

temperature, relative to

the RTNDT of the material

• It was defined as a

lower bound of

dynamic and crack

arrest toughness

𝐾𝐼𝑅 = 26,8 + 12,445 ∙ exp 0,0145 ∙ (𝑇 − 𝑅𝑇𝑁𝐷𝑇)

Welding Research Council Bulletin, WRC-175, 1972

03/09/2018

The Nil Ductility Reference Temperature RTNDT is

determined according to the ASME Code Section III,

NB-2331 as follows:

▪ Determine a temperature TNDT by Drop Weight Tests

▪ Test three Charpy V-notch (CVN) specimens in the T-L (i.e.,

weak) orientation at TNDT + 60 ºF (TNDT + 33 ºC);

• Each specimen must exhibit a minimum of 50 ft-lb (68 J) energy

and 35-mil (0.89 mm) lateral expansion

• If so, then TNDT is the reference temperature RTNDT

▪ If one or all specimens fail to meet the acceptance criteria, test groups of three Charpy specimens at progressively higher

temperatures till criteria are met

• The temperature at which the 35-mil and 50 ft-lb criteria are met is

defined as the TCv

▪ The RTNDT is the higher of TCv – 60 ºF (TCv – 33 ºC) and TNDT

RTNDT definition


RTNDT definition

13

Drop Weight specimen (ASTM E 208) Charpy V specimen (ASTM E 23)


Neutron irradiation reduces the fracture toughness of

the RPV materials

This effect reduces the operating window

Effect of neutron irradiation


Surveillance programs (Appendix H of 10 CFR 50) are

implemented to monitor the radiation-induced

embrittlement

This ageing mechanism is cumulative;

• P-T limit curves must be periodically updated

US NRC Regulatory Guide 1.99, Revision 2 contains

the methods for determining radiation embrittlement

of reactor vessel materials

The embrittlement effect is accounted for through

an increase of RTNDT



The Adjusted RTNDT (ART) is calculated by:

𝐴𝑅𝑇 = Initial 𝑅𝑇𝑁𝐷𝑇 + ∆𝑅𝑇𝑁𝐷𝑇 +MARGIN

where,

▪ Initial 𝑅𝑇𝑁𝐷𝑇 is the 𝑅𝑇𝑁𝐷𝑇 of the unirradiated material

▪ ∆𝑅𝑇𝑁𝐷𝑇 is the mean value of the adjustment of 𝑅𝑇𝑁𝐷𝑇 due to

irradiation

• Depends on the fluence and the material chemistry

▪ MARGIN is a term that accounts for uncertainties:

MARGIN = 2 ∙ 𝜎𝐼2 + 𝜎∆

2

▪ where 𝜎𝐼 y 𝜎∆ are the deviations associated to the

Initial 𝑅𝑇𝑁𝐷𝑇 and ∆𝑅𝑇𝑁𝐷𝑇 respectively.



In mid 1980’s, an Appendix G (initially identical to

that of ASME Section III) was incorporated into

Section XI for obtaining allowable (P-T) limits curves

for heat-up, cooldown and pressure test to prevent

fracture of the RPV and other ferritic pressure

retaining components

Several updates were introduced in subsequent

years

▪ Use of circumferentially oriented ¼-thickness (and ¾-thickness)

assumed reference flaw for vessel with only circumferential

welds

ASME Section XI, Appendix G


▪ Use of 𝐾𝐼𝑐 reference fracture toughness (instead of 𝐾𝐼𝑅) for P-T

limit curves

• 𝐾𝐼𝑐 is the lower bound, plane strain, crack initiation fracture

toughness as a function of temperature, relative to the RTNDT of the

material

• Use of 𝐾𝐼𝑐 is justified by:

o Use of historically large margins to cover uncertainties is no longer

necessary

o No evidence of critical flaw sizes in reactor vessels

o No evidence of local brittle zones in vessel materials

o Loading rates are slow (static); thus, no need to use a dynamic fracture

toughness curve

o Improvements in fracture mechanics analyses confirm large safety

margins

ASME XI Appendix G updates




▪ Improved formulas for the evaluation of stress intensity factors

𝐾𝐼𝑚 and 𝐾𝐼𝑡 for the vessel shell

▪ Improved formulas for the evaluation of stress intensity factors

at nozzle inner corner (ASME Section XI 2013 Edition)

▪ Method for determining Low Temperature Overpressurization

Protection (LTOP) enable temperature



For RPV shell cylindrical regions remote from disconti-

nuities, the allowable pressure for each temperature

of the coolant is determined by

(𝑆𝐹) ∙ 𝐾𝐼𝑚 + 𝐾𝐼𝑡 < 𝐾𝐼𝑐

▪ 𝐾𝐼𝑚 is the stress intensity factor (SIF) caused by membrane

(pressure) stress

▪ 𝐾𝐼𝑡 is the SIF caused by thermal gradients through the vessel

wall (wall thickness dependent);

▪ 𝑆𝐹 = 2 for Level A and Level B Service Limits (Heat-up &

Cooldown)

▪ 𝑆𝐹 = 1.5 for hydrostatic and leak test conditions when the

reactor core is not critical

Basic equations


For flanges and shell regions near geometric discon-

tinuities, the allowable pressure for each

temperature of the coolant is determined by:

𝑆𝐹 ∙ 𝐾𝐼𝑚 + 𝐾𝐼𝑏 𝑝 + 𝐾𝐼𝑚 + 𝐾𝐼𝑏 𝑠 < 𝐾𝐼𝑐

▪ 𝐾𝐼𝑚 is the SIF due to membrane stress

▪ 𝐾𝐼𝑏 is the SIF due to bending stress

▪ Subindices 𝑝 and s indicate primary and secondary stresses,

respectively

• For the purpose of this evaluation, stresses resulting from bolt

preloading are considered primary

▪ 𝑆𝐹 = 2 or 𝑆𝐹 = 1.5 as above

Basic equations


The postulated

defect is circum-

ferential in shape,

and shall be located

at the corner of the

nozzle and the

cylindrical shell (RPV

wall)

Analysis of nozzles


The allowable pressure for each temperature of the coolant is determined by:

(𝑆𝐹) ∙ 𝐾𝐼𝑝 + 𝐾𝐼𝑡 < 𝐾𝐼𝑐

▪ 𝐾𝐼𝑝 is the SIF caused by pressure plus external loading on the nozzle end

▪ 𝐾𝐼𝑡 is the SIF caused by thermal gradients through the thickness (cross section)

The stress distributions along the 45º path should be fitted by a 3rd degree polynomial:

𝜎 𝑥 = 𝐴0 + 𝐴1 ∙ 𝑥 + 𝐴2 ∙ 𝑥2 + 𝐴3 ∙ 𝑥3

▪ 𝑥 is the distance from the surface into the cross section

Analysis of nozzles


The SIF must be calculated as follows (ORNL/TM-

2010/246):

𝐾𝐼 = 𝜋 ∙ 𝑎 ∙

0.723 𝐴0 + 0.5512𝑎

𝜋𝐴1 + 0.462

𝑎2

2𝐴2

+ 0.4084𝑎3

3𝜋𝐴3

¼ T depth flaw bounds flaw shape and crack front

effects of smaller flaws

Smaller flaw can be used if effects of flaw shape and

variation of 𝐾𝐼 along the crack front are considered

Analysis of nozzles


Perform thermal analysis of the vessel wall and

calculate through-wall temperature distributions

along heat-up and cooldown

Perform stress analysis of the vessel and calculate

thermal and pressure stresses

Perform fracture mechanics analysis of the vessel

beltline materials and calculate crack tip SIF (𝐾𝐼)and determine irradiated material fracture

toughness

Determine allowable pressure vs. temperature for

each beltline material and take worst case which

may result in a composite curve

Steps in calculating P-T curves


Internal pressure produces tensile stresses on the

assumed inside ¼ T flaw and outside ¾ T flaw that

tend to open the flaw

Heat-up process produces thermal stresses on the

assumed inside surface ¼ T flaw that are

compressive and tend to counteract the tensile

stresses from internal pressure

However, thermal stresses on the assumed outside

surface ¾ T flaw are tensile and reinforce any

pressure stresses, tending to open the flaw, and

¼ T location has a higher RTNDT due to irradiation

than ¾ T location

Heat-up


Each data point on the heat-up curve for any heat-

up rate must be the most limiting pressure between:

▪ steady-state (¼ T flaw depth) and the finite heat-up rate (¼ T

and ¾ T flaw depths)

Heat-up


Internal pressure produces tensile stresses on the

assumed inside surface ¼ T flaw that tend to open

the flaw

Cooldown process produces thermal stresses on the

assumed inside surface ¼ T flaw that are tensile and

tend to reinforce the tensile stresses from internal

pressure

¼ T location has also a higher RTNDT due to irradiation

Each data point on the cooldown curve for any

cooldown rate must be the most limiting pressure

between steady-state and the finite cooldown rate

Cooldown


Hydrostatic and leak test are calculated considering

• ¼ T flaw due to higher irradiation

• 𝑆𝐹 = 1.5 on primary stress

• Isothermal conditions (𝐾𝐼𝑡 = 0)

If fuel has not been loaded into the reactor vessel

prior to performing the hydrostatic tests, the test must

be performed at a temperature not lower than RTNDT

+ 60 °F (RTNDT + 33 °C)

Hydrostatic and leak test


Administrative margins related to accuracy and

uncertainty of instruments should be used (i.e.,

narrow range vs. wide range instruments); typically

410 kPa (60 psi) and 6 °C (10 °F)

Instrumentation uncertainties


10 CFR 50, Appendix G requirements for closure

flange:

▪ During heat-up, the closure flange region (stressed by the bolt

preload) may become limiting for P-T limits

• For boltup the minimum temperature is the RTNDT of closure flange

zone

• However, higher values are usually adopted

▪ For core non critical

• The metal temperature of the closure flange zone must be greater

than RTNDT +120 °F (RTNDT + 66 °C) for P > 20% of the preservice hydro

test pressure (i.e., about 621.25 psi or 4285 kPa)

▪ For core critical

• The metal temperature of the closure flange zone must be greater

than RTNDT +160 °F (RTNDT + 89 ºC) when the pressure exceeds 20% of

the preservice hydro test pressure

Additional requirements (10 CFR 50)


10 CFR 50, Appendix G requirements for core critical:

▪ P-T limits must be 40 °F (22 ºC) above any normal heat-

up/cooldown (core not critical) limits

▪ For any pressure, the core critical limit temperature must be at

least that required for the pressure test limits

Additional requirements (10 CFR 50)


-15

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0 50 100 150 200 250 300 350

Ind

ica

ted

Pre

sisu

re (p

sig

)

Indicated Temperature ( F)

Pressure-Temperature Heatup Curve for 54 EFPY

UNACCEPTABLE

OPERATION

Limit for heatup rates up to 60 F/h

Limiting Material: Core Beltline Plate(RTNDT)1/4T at 54 EFPY: 160 °F(RTNDT)3/4T at 54 EFPY: 130 °F

Instrumentation uncertainties:- Pressure: 60 psig

- Temperature: 10 F

-14,7

Criticality Limit based on a inservice hydrostatic test temperature of 230,4 ºF for

a period of 54 EFPY

Hydrostatic Test Limit

-14,7 psig Limit for Vacuum Refill of RCS

ACCEPTABLE OPERATION

40 ºF

Temperature for boltup

Sample curve


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0 25 50 75 100 125 150 175 200 225 250 275

Ind

icat

ed

Pre

ssu

re (

psi

g)

Indicated Temperature ( F)

Pressure-Temperature Cooldown Curve for 54 EFPY

Límits for different cooldown rates (°F/h):

-14,7

0

2060

100

-14,7 psig Limit for Vacuum Refill of RCS

Instrumentation uncertainties:- Pressure: 60 psig

- Temperature: 10 F

Limiting Material: Core Beltline Plate(RTNDT)1/4T at 54 EFPY: 160 °F(RTNDT)3/4T at 54 EFPY: 130 °F

UNACCEPTABLE OPERATION

ACCEPTABLE

OPERATION

Closure flange notch

Sample cooldown curve


Historically, P-T limits only considered the region

directly adjacent to the core (beltline)

As neutron embrittlement levels increase in the

existing reactor vessels, other materials outside of the

traditional beltline are expected to be analyzed for

reactor vessel integrity

For plants of American design, changes in the

fracture toughness properties of RPV materials have

been demonstrated to occur at neutron fluence

levels as low as 1x1017 n/cm2 (E > 1 MeV)

RPV materials whose predicted EOL fluence reaches

that level constitute the “extended beltline”

Extended beltline


US NRC issued a Regulatory Issue Summary RIS 2014-

11(1)

• Intent was to provide clarification on development of P-T limits

• RPV nozzles, penetrations, and other discontinuities have

complex geometries that may exhibit significantly higher

stresses than those for the reactor vessel beltline shell region

(cylindrical)

▪ The higher stresses can potentially result in more restrictive P-T limits

• All ferritic materials projected to experience fluence levels

greater than 1x1017 n/cm2 (E > 1 MeV) for the period of

operation should be considered for P-T limit analysis

(1) “Information on Licensing Applications For Fracture

Toughness Requirements For Ferritic Reactor Coolant Pressure Boundary Components”

Extended beltline


The indexing parameter RTNDT of ASME reference

curves 𝐾𝐼𝑅 and 𝐾𝐼𝑐 is, some cases, overly conserva-

tive in relation to the real toughness of RPV steels

The Master Curve method can provide a directly

measured fracture toughness temperature index, as

well as statistically derived tolerance bounds for both

unirradiated and irradiated steels

ASME Code Case N-629 defines an alternative index 𝑅𝑇𝑇0 for the reference toughness 𝐾𝐼𝑅 and 𝐾𝐼𝑐

𝑅𝑇𝑇0 = 𝑇0 + 35℉ = 𝑇0 + 19.4 ℃

Where 𝑇0 is obtained according to ASTM E 1921

Application of Master Curve


This definition of 𝑅𝑇𝑇0 appropriately bounds available data:

ASME Code Case N-629 is now incorporated in Section XI Appendix G

39SOTERIA Training School - September 2018 - Polytechnic University of Valencia

Application of Master Curve

03/09/2018

By the late 1970s, 29 events occurred that produced

pressure excursions above the P-T limits during PWR

operation at lowtemperature

▪ Service experience indicates most events are isothermal and

occur between 100 – 200 °F (38 – 93 °C)

Low Temperature Over-pressurization Protection

(LTOP) systems must be in place to protect the vessel

against brittle fracture due to high pressure (i.e.,

water solid) operation while at low temperature

▪ Protects the low end of the Appendix G curves by

implementing P-T setpoints in pressurizer relief valves

Low Temperature Over-pressurization

Protection (LTOP)

4003/09/2018 SOTERIA Training School - September 2018 - Polytechnic University of Valencia

In Appendix G of Section XI the LTOP enable

temperature is defined as the higher of

▪ 200 ºF (93 ºC)

▪ The coolant temperature corresponding to a metal

temperature (1/4 T) of RTNDT + 50 ºF (RTNDT + 33 ºC)

4103/09/2018 SOTERIA Training School - September 2018 - Polytechnic University of Valencia

Low Temperature Over-pressurization

Protection (LTOP)

P-T limits operating curves are designed to ensure that there is an adequate margin against component failure from the combination of pressure, thermal stresses and flaws that may exist in the component

Normally, are calculated for a given value of effective full power years (EFPY) which corresponds to a maximum fluence and limiting ART value for the specified EFPY

If new surveillance data, fluence evaluations, or plant capacity factor causes this ART value to be exceeded, the curves may not be bounding for the EFPY

Curves are updated periodically and as required to remain bounding

Summary


THANKS FOR YOUR ATTENTION

QUESTIONS?


Training School, 3 - 7 September 2018

Polytechnic University of Valencia (Spain)

Documents

PRESSURE-TEMPERATURE LIMIT CURVES